To find out what fraction of the entire assignment Celeste's mom checked, we need to multiply the fractions of the problems Celeste completed and her mom checked.
Celeste completed \( \frac{5}{6} \) of her science problems, and her mom checked \( \frac{2}{3} \) of those problems.
The fraction of the assignment that her mom checked is given by:
\[ \text{Fraction checked} = \left( \frac{5}{6} \right) \times \left( \frac{2}{3} \right) \]
Now, multiply the two fractions:
\[ \frac{5 \times 2}{6 \times 3} = \frac{10}{18} \]
Now, simplify \( \frac{10}{18} \):
\[ \frac{10}{18} = \frac{5}{9} \]
Thus, the fraction of the assignment that Celeste's mom checked is \( \frac{5}{9} \).
The answer is \( \frac{5}{9} \).